-
Advances in the modeling of laser direct metal depositionAndrew
J. Pinkerton
Citation: Journal of Laser Applications 27, S15001 (2015); doi:
10.2351/1.4815992 View online: http://dx.doi.org/10.2351/1.4815992
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Published by the Laser Institute of America
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Advances in the modeling of laser direct metal deposition
Andrew J. Pinkertona)
Department of Engineering, Lancaster University, Bailrigg,
Lancaster LA1 4YR, United Kingdom
(Received 7 March 2013; accepted for publication 4 July 2013;
published 9 December 2014)
This paper provides a review of the current state of the art in
modeling of laser direct metal
deposition and cladding processes and identifies recent advances
and trends in this field. The
different stages of the process and the features, strengths and
weaknesses of models relating to them
are discussed. Although direct metal deposition is now firmly in
the industrial domain, the benefits to
be gained from reliable predictive modeling of the process are
still to be fully exploited. The genuine
progress there has been in this field in the last five years,
particularly in discretized modeling, means
modeling cannot be overlooked as an enabling method for academia
and industry, but there is still
more work to be done.VC 2014 Laser Institute of America.
Key words: laser, deposition, cladding, model, simulation,
review
I. INTRODUCTION
Even finding consensus on a name for the laser direct
metal deposition (laser cladding, direct metal deposition,
direct laser deposition, directed light fabrication, laser
pow-
der fusion, laser engineered net shaping, etc) process has
to-date proved impossible. It is, thus, of no surprise that
there
is such a disparate range of models of the process. But this
must be viewed as a positive thing: they are advancing the
modeling of the different stages of the deposition process
and, excitingly, the complete process in umpteen ways.
Academic attention to process modeling continues to
increase but has still been outpaced by the growth of
additive
manufacturing in general, which has seen double digit growth
for 15 of its 24 yrs.1 Figure 1 illustrates the growth of
laser
direct metal deposition (LDMD) modeling of all types and
models describing themselves as numerical in the title or
keywords in particular. Empiricalstatistical and analytical
models were almost exclusively used until the advent of nu-
merical and hybrid analyticalnumerical models, which prin-
cipally refers to those employing the discretization method,
over the last 10 years.
II. EMPIRICALSTATISTICAL MODELS
Empiricalstatistical models have been produced since
the advent of LDMD as they avoid the complexity of analyz-
ing the physical phenomena of the process itself. Direct
metal deposition is typically described as having three
primary process inputs of laser power, powder mass flow
rate, and traverse speed. Most models have concentrated on
relating these to final track geometry, typically using
regres-
sion methods to relate input and response variables (Table
I).
Other models have addressed less common response parame-
ters such as, clad angle,2 deposition efficiency,3 and
uniform-
ity index (clad area / (track width height)),4 while othershave
used less common experimental designs, for example
Hartleys plan.5 The process and response variables have
also been related in other ways: Toyserkani et al. proposedElman
recurrent neural network modeling6 and Hua and
Choi proposed use of fuzzy logic to adaptively predict and
control clad height as a function of laser power.7
However, examination of Table I shows an inherent dis-
advantage of the empiricalstatistical approach. These mod-
els give broadly similar but seldom exactly the same
results,
even though in many cases they are based on similar meth-
ods. Qi et al.8 suggested 1214 factors with a strong effecton
final part characteristics, so the models are, at least to
some extent, specific to the values of factors that were
fixed.
Despite design of experiment methods, models have not
significantly advanced the number of process variables they
are able to account for in the recent past, and limitations
of
experimental time mean there are no indications that they
will in the future. There is thus so real sign that this
model-
ing method will change significantly in the future.
III. APPROACHES TO THE PHYSICAL MODELING OFDIRECT METAL
DEPOSITION
The large number of variables and diverse phenomena
within the LDMD process means the complete process is
commonly considered in stages and different physical
models applied at each stage. This introduces intermediate
variables that need to be carried over from one stage of the
process to the other. Figure 2 illustrates how the complete
process is typically broken down physically and Fig. 3 the
corresponding model-part this creates. Advances in physical
modeling of the different process stages and the process as
a
whole are then considered.
A. Models of the powder stream process
The powder stream and powder stream processes are
highly significant for track formation as they directly
affect
beam attenuation and powder distribution, velocity, and tem-
perature at substrate height. The spatial distribution of
pow-
der particles beneath a coaxial nozzle and their interaction
a)Electronic mail: [email protected]. Telephone: 44
(0)1524593547.
1042-346X/2015/27(S1)/S15001/7/$28.00 VC 2014 Laser Institute of
AmericaS15001-1
JOURNAL OF LASER APPLICATIONS LASER ADDITIVE MANUFACTURING
FEBRUARY 2015
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with the laser beam have traditionally been described by
ana-
lytical methods, typically by approximating the stream shape
to an idealized Gaussian distribution and the particle path
to
extensions of the nozzle passages (e.g., Refs. 1719).
Attenuation has been taken care of via the BeerLambert
law and powder temperature from total time of a particle
within the beam.17 The most advanced analytical models can
now account for variable particle velocity20 and return the
values of powder distribution at the substrate level, beam
attenuation, and powder temperature.21 The analytical mod-
els are well tested and still widely used as good approxima-
tions but tend to rely on estimated or experimental values
for
variables such as powder stream divergence.
The use of computational fluid dynamics (CFD) methods
is not in itself very new: Lin produced realistic model of
mass
flow in the powder stream in 2000. The numerical method
allows stream modeling without many of the assumptions
mentioned above and has shown assumptions like straight
powder paths and constant powder speed to be approximations
rather than reality. Models of this type have increased
greatly
in sophistication in the last few years. Pan and Liou22,23
pro-
duced a stochastic model for initial trajectory of the
particle
when entering the powder stream and several authors have
produced CFD models of powder flow in the nozzle and
powder stream with different degrees of complexity.2426
The most advanced models of this type now include the
nozzle and stream, account for the size and shape of
particle
using a shape factor,27 and provide both particle heating
and mass flow results28 (Fig. 4).
Further, the LDMD process must build on a solid wall or
substrate, but the effect of this on the gas and powder
flows
has only just been considered. The gasliquid interface geo-
metry input to the powder stream model shown in Fig. 3
has thus been neglected. Kovalov et al.29 used an advancedCFD
model of a three passage nozzle, similar to that of Wen
et al.,28 to consider the substrate effect. The flow was
verydifferent from that of a free stream with vortex flows
form-
ing above the substrate (Fig. 5). Focussing on powder flow,
Zekovic et al.30 modeled powder flow from a LENS nozzleusing the
ke turbulent model and showed changes in pow-der concentrations
below the nozzle due to ricocheting par-
ticles when a substrate was in place. Ibarra-Medina and
Pinkerton31 showed the same effect with a coaxial nozzle
and also drew attention to the implications for powder heat-
ing and beam attenuation. This type of model was firmly
confirmed as state of the art by a verified CFD model based
on the same assumptions as that of Zekovic et al. byTabernero et
al. in 2010.32,33
Modeling of the powder stream process is advancing
rapidly. Models with the substrate in place would probably
benefit from further testing to establish under what circum-
stances the effects they reveal are significant. However,
they
FIG. 1. Growth in the publication of laser cladding and metal
deposition
models per year since 1985 [based on SCOPUS data, title and
keyword
searches, absolute values give an estimate only].
TABLE I. Empiricalstatistical relationships between track
geometry and LDMD primary process variables (P laser power, F
powder mass flow rate,V traverse speed, RSM response surface
method, RA regression analysis).
Primary process response variable
Work Track height Track width Track depth or melt area
Kumar (Ref. 9) P1/4 V1F1/4 Sun (Ref. 10) (ANOVA, RSM) P, V, F,
PF, P2 P, V, F, PV, V2 P, V, F, P2, F2
El Cheikh (Ref. 11) P1/4 V1F3/4 P3/4V1/4 Ln(P4/5F1/4)Davim (Ref.
12) (ANOVA, RA) P, V, F P, V, F P, V, F
Ocelik (Ref. 13) V21F PV1/2 P2V1/2
Davim (Ref. 14) P, V, Fa P, FV, Fa P, Fa
De Oliveira (Refs. 10 and 15) (RA) FV21 PV1/2 PV1/3F1/3
Felde (Ref. 16) P1/2 V1F1/2
aTaking confidence values above 5%.
FIG. 2. (Arbitrary) Stages of direct metal deposition or laser
cladding in
terms of physical limits.
S15001-2 J. Laser Appl., Vol. 27, No. S1, February 2015 Andrew
J. Pinkerton
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could mean the ubiquitous free stream powder model has
been superceded.
B. Models of the melt pool process
Models of the melt pool are at the heart of the deposition
process. The typical assumptions of an analytical model are
quasistationary conditions, a mathematically simple sub-
strate shape (typically semi-infinite or thin plate), and
geo-
metrically simple melt pool boundaries, either combinations
of half ellipses34,35 (based on moving source heat
theory36,37)
or circles11,38,39 (assuming surface tension normal to the
sur-
face shapes the molten pool). Despite these necessary
simpli-
fications, there have been some recent informative models
and ones covering the effect of powder types and laser focus
points on wall layer formation4042 and on combining laser
and induction heating for hybrid rapid cladding43 stand out.
The ability to use iterative numerical solution methods for
analytically formulated models44,45 has also reduced the
con-
straints of using this modeling method.
Numerical discretized methods more naturally account
for inhomogeneity in problems but in practice makes calcu-
lating melt pool geometry an exacting task. Therefore, mod-
els using this method have tended to focus on calculating
the
temperature distributions and thermal history of the final
part.4648 Early models applied a heat flux to an unchanging
surface (e.g., Ref. 49), but more recent models have come to
rely on the element activation (birth) methodology,
although Ye et al.48 have also demonstrated use of the
alter-native fixed boundary method (after Refs. 50 and 51).
Models of this type differ in the way heat is added to the
sub-
strate: using a heat flux,47 activating the new elements at
the
liquidus temperature (assuming particles at this temperature
FIG. 3. Subprocesses and process variables corresponding to the
physical stages of deposition shown in Fig. 2.
FIG. 4. Modeled coaxial powder flow and heating (Ref. 28).
FIG. 5. Gas jet flows onto a flat substrate with a triple
coaxial nozzlevelocity
field and gas streamlines (Courtesy of Professor O. Kovalev,
Theoretical and
experimental investigation of gas flows, powder transport and
heating in
coaxial laser direct metal deposition (DMD) process, J. Therm.
Spray
Technol. 20, 465478 (2011). Copyright 2011, Springer).
J. Laser Appl., Vol. 27, No. S1, February 2015 Andrew J.
Pinkerton S15001-3
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and 100% attenuation)48,5254 or using a combination of the
two methods.55 Kumar and Roy56 presented a two-
dimensional finite volume model that explicitly returns
solid-
ification front information such as thermal gradient
suitable
for use by a solidification model.
The model types above have the failing of not explicitly
calculating fluid flows within the melt pool. Some compen-
sate for it by increasing conductivity within the melt pool.
This can be done either isotropically or anisotropically57
but
requires arbitrary or experimentally set enhancement
factors.
A more advanced form of model, incorporating fluid flow
effects and a free-surface method to predict the melt pool
and subsequent track shape, has now emerged.5861 The
most recent and advanced models by Morville et al.59 explic-itly
track the dynamic shape of the free surface using an arbi-
trary Lagrangian Eulerian (ALE) moving mesh and
realistically predict thin wall growth including the
character-
istic shapes near the limits of the wall.
Despite the importance of this work, probably the state
of the art in melt pool modeling has come from models that
encompass both the powder stream and melt pool processes.
Toyserkani et al.62,63 began by proposing a single
modelencompassing the two but with the two processes largely
decoupled. More complex analyticalnumerical and numeri-
cal models have followed.8,61,6473
The levels set method was used by Qi et al. to simulateformation
of a single track8 and by He et al. to simulate twooverlapping clad
tracks64,65 using an hybrid analytical and nu-
merical discretized model. The powder stream was treated
ana-
lytically as Gaussian and the beam subject to BeerLambert
attenuation, while the melt pool simulations were fully
numeri-
cal and incorporated Marangoni and capillary effects. Peyre
et al.66 used a similar combination of an analytical
powderstream model and a numerical finite element (FE) method
for
heat flow within the built part but also incorporated an
approach to model the deposition of vertically aligned
tracks.
In further recent work aimed at this subject by Gharbi,
Peyre
et al.72,73 a rare analytical model covering both powder
streamand melt pool correlates thin wall surface finish to melt
pool
size for different thermo-capillary behaviors.
Different from these are the continuum models of Wen
and Shin67 and Ibarra-medina et al.,74 which contain no
ana-lytical component. Wen and Shin modeled the LENS pro-
cess, incorporating Marangoni and Capillary effects, and
used a level-set method for melt pool surface tracking (akin
to Han et al.75). Gas flow in the powder stream was taken
asturbulent, described by the ke model as reported in anotherpaper
dedicated to this subject.67 The model was also applied
to two overlapping tracks,68 off-axis deposition69 and clad-
ding with an additional hard particle phase.70 The model of
Ibarra-medina et al. incorporated the same effects but
con-sidered an annular nozzle and used the volume of fluid
(VOF) method (Fig. 6).
In summary, models have advanced by ceasing to consider
purely thermodynamic effects and incorporating fluid
dynamics
effects in a predictive way. This means modeling of the melt
pool process is advancing as quickly as that of the powder
stream process. Most benefit in the immediate future would
come from better integration of these state-of-the-art melt
pool
models with other subprocess models of the powder stream and
final properties.
C. Models of microstructure, stress, and finalgeometry
Obtaining final part properties is the ultimate aim of the
modeling process. The core ones can be considered as final
geometry (including distortion), microstructure, and stress
distributions. Many other properties can be derived from
these. To obtain the distribution of residual stress, many
FIG. 6. Simulated deposition of a thin wall using a multistage
model (Ref. 76).
S15001-4 J. Laser Appl., Vol. 27, No. S1, February 2015 Andrew
J. Pinkerton
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models consist of a discretized melt pool model of the type
described in Sec. III B and exploit the functionality of
commer-
cial software such as ANSYS (e.g., Refs. 77 and 78) and
ABAQUS
(e.g., Ref. 79). The stress is affected by variables such as
layer
height,80 substrate geometry and temperature fed from the
pre-
vious model-part81,82 and from those such as phase
transforma-
tion calculated within this process stage.83 Models of this
type
are difficult to verify but work by Labudovic et al.,84 using
ahigh speed camera and off-line metallographical and x-ray dif-
fraction analyses, and by Rangaswamy et al.85 and Moatet al.,86
using neutron diffraction, has facilitated this.
As a whole, LDMD microstructure modeling is a younger
area than stress modeling. Investigations in this area have
tended to be experimental and concentrate on high perform-
ance materials, particularly titanium8790 and
superalloys.9195
Phase-microstructure models are again usually based on dis-
cretized melt pool model of the type described in Sec. III
B,
with added subroutines to relate the temperature history at
each node to the final material state. Authors such as Wang
et al.96 have used continuous cooling transformation dia-grams;
however, Colaco and Vilar suggest that the nonequili-
brium solidification that can occur in LDMD means that
modified expressions are needed.97 Papers in this area have
considered deposition of a range of materials including
stain-
less steels,52,96 medium carbon steel,98 and titanium
alloys,55
each using thermo-metallurgical phase transformation models
specific to the material. However, work has not been limited
to purely metallic coatings and phase analysis: Lei et al.
con-sidered composite coatings on Ti6Al4V alloys99 using the
WilsonFrenkel growth law to relate the modeled temperature
distribution and history in a test part to the size of TiC
par-
ticles that formed. In other work, Pirch et al. concentrated
oncalculating dendritic growth direction in multitrack depos-
its.100 Models in this area have advanced by expanding both
the parameters they consider and return. The residual stress
models of Bruckner et al.101 and Alimardani et al.102
includedecoupled analytical model of the powder stream which
ena-
ble them to also calculate an (idealized) track geometry.
The
former also accounts for phase effects.
IV. SUMMARY
There are some genuinely new analytical models being
produced but the proportion of numerical models, particu-
larly those based on the discretization method, in this field
is
continuing to increase. Probably, the most interesting
devel-
opment in the last few years has been the growth in analyti-
cal discretized and discretized models that span multiple
stages of direct metal deposition. Further development of
this towards a usable, unified model is an exciting
prospect.
But models have many uses.103 An overall process
model (red to red in Fig. 3) could be used for process plan-
ning or design, analytical models are the classic way to
increase understanding of an unfamiliar aspect of the pro-
cess, and there are other opportunities for modelling in
con-
trol that have not even been touched on here.104110
There is still plenty of opportunity for genuinely better
models and these could benefit the laser community in multi-
ple ways.
ACKNOWLEDGMENTS
The author is grateful to the authors and publishers who
have allowed him to use their figures in this paper to exam-
ple leading models in the field. Thanks also to Milan Brandt
for giving me this opportunity and to colleagues working on
the INLADE project over the last few years.
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